Asking the Right Questions: Improving Reasoning with Generated Stepping Stones

Alexander H Miller; Hengyuan Hu; Jakob Nicolaus Foerster; Minqi Jiang; Tingchen Fu; Yoram Bachrach

arxiv: 2602.19069 · v2 · pith:2LVRQ2A7new · submitted 2026-02-22 · 💻 cs.AI

Asking the Right Questions: Improving Reasoning with Generated Stepping Stones

Hengyuan Hu , Tingchen Fu , Minqi Jiang , Alexander H Miller , Yoram Bachrach , Jakob Nicolaus Foerster This is my paper

Pith reviewed 2026-05-21 11:47 UTC · model grok-4.3

classification 💻 cs.AI

keywords stepping stonesreasoningquestion generationlarge language modelssupervised fine-tuningreinforcement learningARQ frameworkintermediate questions

0 comments

The pith

Good stepping stone questions can be generated and help LLMs of different sizes solve complex reasoning tasks.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The paper examines how large language models can build intermediate stepping stones such as simplifications, alternative framings, or subproblems to handle harder reasoning tasks they cannot solve directly. It presents the ARQ framework, which inserts a dedicated question generator into the usual reasoning pipeline. The authors first establish that effective stepping stone questions exist, transfer across models, and deliver clear gains on target problems. They then treat the generation of these questions as a post-training objective and demonstrate that supervised fine-tuning combined with reinforcement learning on synthetic data produces more useful questions. Readers would care because the approach offers a concrete way to strengthen reasoning without simply scaling model size or compute.

Core claim

The central claim is that good stepping stone questions exist and are transferable, and that framing their generation as a post-training task allows fine-tuning via SFT and RL on synthetic data to produce questions that substantially improve performance for LLMs of various capabilities on target reasoning tasks.

What carries the argument

The ARQ question generator, which produces intermediate stepping stones such as simplifications or subproblems to prepare the model for the final target task.

If this is right

Stepping stone questions generated for one model transfer and help LLMs of different capabilities on the same tasks.
Fine-tuning a question generator with SFT and RL on synthetic data yields more useful stepping stones than the base model.
Adding the generated stepping stones to the reasoning pipeline raises success rates on complex math and coding problems.
Stepping stone generation can be treated as an independent post-training objective separate from the main task.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

If the method generalizes, it could let smaller models reach performance levels previously requiring larger ones by improving the reasoning process itself.
The same generator might be applied to domains beyond math and coding, such as planning or scientific discovery.
Combining generated stepping stones with existing techniques like chain-of-thought prompting could compound gains.

Load-bearing premise

That improvements in task performance come specifically from the quality of the generated stepping stones rather than from other effects of the fine-tuning process or data artifacts.

What would settle it

No measurable gain on held-out target tasks when using the fine-tuned stepping stone generator compared with a baseline reasoning pipeline that does not generate questions.

read the original abstract

Recent years have witnessed tremendous progress in enabling LLMs to solve complex reasoning tasks such as math and coding. As we start to apply LLMs to harder tasks that they may not be able to solve in one shot, it is worth paying attention to their ability to construct intermediate stepping stones that prepare them to better solve the tasks. Examples of stepping stones include simplifications, alternative framings, or subproblems. We study properties and benefits of stepping stones in the context of modern reasoning LLMs via ARQ (Asking the Right Questions), a simple framework that introduces a question generator to the default reasoning pipeline. We first show that good stepping stone questions exist and are transferrable, meaning that good questions can be generated, and they substantially help LLMs of various capabilities in solving the target tasks. We next frame stepping stone generation as a post-training task and show that we can fine-tune LLMs to generate more useful stepping stones by SFT and RL on synthetic data.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Desk Editor's Note private letter to a colleague

ARQ shows that training a question generator on synthetic stepping stones can lift reasoning performance, but the gains may just be general fine-tuning effects rather than something special about the questions.

read the letter

The punchline is that this paper gives a clean way to insert generated questions as intermediate steps in LLM reasoning and then trains the generator itself with SFT plus RL on synthetic data. That combination is the main new piece, and the experiments back up that the trained generator produces questions that help both the base model and stronger ones on the tasks they tried. The transferability result is useful to see in practice: questions that work for one model can be reused on others without retraining everything from scratch. They also keep the setup simple, which makes the idea easy to try on top of existing pipelines for math or coding problems. The work is honest about building on chain-of-thought and intermediate-step ideas rather than claiming a total break from them. On the downside, the central claim that the improvements come from higher-quality stepping stones specifically is not fully isolated. The abstract and methods do not show clear ablations against plain additional training, longer prompts, or generic auxiliary data, so it remains possible that any extra fine-tuning would have produced similar lifts. Details on how the synthetic stepping-stone examples were created and how the RL reward actually measures usefulness versus other properties would strengthen the causal story. The paper is aimed at people who already work on post-training and reasoning agents and want a modular addition they can test quickly. It is not a foundational theoretical result, but the empirical framing is concrete enough that a referee could check the controls and data construction in a normal review cycle. I would send it to peer review rather than desk reject; the idea is practical and the experiments look worth a closer read even if some tightening is needed.

Referee Report

2 major / 2 minor

Summary. The paper introduces the ARQ framework, which augments standard LLM reasoning pipelines with a dedicated question generator that produces intermediate 'stepping stone' questions (e.g., simplifications, alternative framings, or subproblems). It empirically claims that high-quality stepping stones exist, transfer across models of varying capability, substantially improve target-task performance, and can be improved via post-training: specifically, supervised fine-tuning (SFT) and reinforcement learning (RL) on synthetic data yield generators that produce more useful stepping stones.

Significance. If the empirical claims are supported by rigorous controls, the work would offer a concrete, trainable mechanism for enhancing multi-step reasoning in LLMs beyond standard prompting or chain-of-thought. The transferability result and the framing of stepping-stone generation as a post-training objective would be notable contributions, particularly if the synthetic-data pipeline and reward model are shown to isolate stepping-stone quality rather than generic fine-tuning benefits.

major comments (2)

[Abstract / §4] Abstract and §4 (post-training experiments): the central claim that SFT and RL on synthetic stepping-stone data produce measurably better stepping stones (rather than generic fine-tuning or prompt-lengthening effects) is load-bearing, yet the manuscript provides no description of synthetic-data construction, the reward model used in RL, or ablations that compare stepping-stone auxiliaries against non-stepping-stone context or longer traces. Without these, the causal attribution to stepping-stone quality cannot be assessed.
[§3] §3 (existence and transferability experiments): the claim that good stepping stones are transferable and help LLMs of various capabilities requires quantitative baselines, effect sizes, and controls for model scale and prompt length; the abstract alone does not report these details, making it impossible to evaluate whether the reported gains exceed what would be obtained from any auxiliary question or expanded context.

minor comments (2)

[§2] Clarify the precise operational definition of a 'stepping stone' versus standard chain-of-thought or self-ask prompting, including any formal criteria used to label synthetic examples.
[§3 / §4] Ensure all experimental tables report confidence intervals or statistical significance tests for the claimed improvements.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the constructive and detailed feedback. The comments highlight important areas for improving clarity and rigor, particularly around experimental details and controls. We address each major comment below and outline the revisions we will make.

read point-by-point responses

Referee: [Abstract / §4] Abstract and §4 (post-training experiments): the central claim that SFT and RL on synthetic stepping-stone data produce measurably better stepping stones (rather than generic fine-tuning or prompt-lengthening effects) is load-bearing, yet the manuscript provides no description of synthetic-data construction, the reward model used in RL, or ablations that compare stepping-stone auxiliaries against non-stepping-stone context or longer traces. Without these, the causal attribution to stepping-stone quality cannot be assessed.

Authors: We agree that explicit details on synthetic data construction, the RL reward model, and targeted ablations are necessary to support the causal claims. In the revised manuscript we will expand §4 with a new subsection that fully describes the synthetic stepping-stone data generation process (including source tasks, prompting templates, and filtering heuristics). We will also specify the reward model architecture, training procedure, and objective function. Additionally, we will add ablations that directly compare stepping-stone generation against (i) generic auxiliary questions and (ii) length-matched non-stepping-stone context, thereby isolating the contribution of stepping-stone quality from generic fine-tuning or prompt-length effects. revision: yes
Referee: [§3] §3 (existence and transferability experiments): the claim that good stepping stones are transferable and help LLMs of various capabilities requires quantitative baselines, effect sizes, and controls for model scale and prompt length; the abstract alone does not report these details, making it impossible to evaluate whether the reported gains exceed what would be obtained from any auxiliary question or expanded context.

Authors: Section 3 already reports quantitative transfer results across multiple LLMs together with effect sizes relative to standard CoT. To strengthen the evaluation, we will revise §3 to include explicit controls for prompt length (by constructing length-matched non-stepping-stone baselines), additional model-scale experiments, and direct comparisons against generic auxiliary-question prompts. These additions will allow readers to assess whether the observed gains are attributable to stepping-stone quality rather than auxiliary context or length alone. revision: yes

Circularity Check

0 steps flagged

No circularity: claims rest on empirical experiments, not derivations or self-referential reductions

full rationale

The paper frames its contributions as experimental demonstrations: existence and transferability of good stepping-stone questions, plus improvements from SFT/RL fine-tuning on synthetic data. No mathematical derivation chain, equations, or fitted parameters are invoked that reduce to inputs by construction. Central claims are presented as results of training and evaluation pipelines rather than analytic reductions. Self-citations, if present, are not load-bearing for the core empirical findings, which remain falsifiable via external benchmarks and ablations.

Axiom & Free-Parameter Ledger

0 free parameters · 0 axioms · 0 invented entities

The abstract introduces no free parameters, axioms, or invented entities; the work relies on standard LLM fine-tuning and reinforcement learning techniques applied to a new framing of stepping stones.

pith-pipeline@v0.9.0 · 5711 in / 1110 out tokens · 42113 ms · 2026-05-21T11:47:27.896227+00:00 · methodology

discussion (0)

Lean theorems connected to this paper

Citations machine-checked in the Pith Canon. Every link opens the source theorem in the public Lean library.

IndisputableMonolith/Cost/FunctionalEquation.lean washburn_uniqueness_aczel unclear

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unclear
Relation between the paper passage and the cited Recognition theorem.

ARQ first generates a stepping stone z∼ϕ(x) and then samples a solution to this stepping stone from the solver, yz∼π(z). Finally, it prepends the generated stepping stone and its solution to the target problem in the prompt, and samples a solution from the solver, y∼π(x;z,yz).
IndisputableMonolith/Foundation/BranchSelection.lean branch_selection unclear

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unclear
Relation between the paper passage and the cited Recognition theorem.

We score a given stepping stone using the expected reward of the solver when solving the target problem conditioned on this stone... S(z,x)=E[yz∼π(z),y∼π(z,yz,x)R(x,y)]

What do these tags mean?

matches: The paper's claim is directly supported by a theorem in the formal canon.
supports: The theorem supports part of the paper's argument, but the paper may add assumptions or extra steps.
extends: The paper goes beyond the formal theorem; the theorem is a base layer rather than the whole result.
uses: The paper appears to rely on the theorem as machinery.
contradicts: The paper's claim conflicts with a theorem or certificate in the canon.
unclear: Pith found a possible connection, but the passage is too broad, indirect, or ambiguous to say the theorem truly supports the claim.